How can I make curves "stick" to a model?
Starting with  version 2.78 you can Draw Freehand Curves.

First create a curve > bezier object in object mode.

Enter edit mode (Tab). You can delete the existing curve segments by pressing A to select all vertices and pressing Delete.

In the Options tab enable the projection depth to surface, that way the drawn curves will stick to the surface of other objects.



Then go to the Create tab and select Draw Curve to draw a curve directly in the 3D viewport.





For more info watch this: https://www.youtube.com/watch?v=tAsUGy7XGOA